Cavitation performance analysis and optimal design of the portable electric-driven axial flow pump

Based on the ISIGHT optimization platform, the impeller parameterization modeling and simulation process of the portable axial flow pump is carried out through CFturbo, ICEM and CFX software, and the impeller is optimized with the help of multi-island genetic algorithm to target the two optimization objectives of efficiency and head. The optimization results show that the hydraulic efficiency increased by 6.3% under design conditions. At the same time, compared with the original solution, the optimized cavitation performance is significantly improved. Additionally, overall entropy production is significantly reduced. Field test results show that the head deviation is 1.42% and the efficiency deviation is 4.52% under design conditions, proving that the optimization results are reliable.


Introduction
With the emergence of global extreme events, the frequency of droughts, urban floods and other disasters has increased sharply in recent years, which has had a great impact on security and economy.Due to its flexibility, portable electric-driven portable axial flow pumps have obvious advantages in dealing with urban waterlogging [1].Improving the efficiency of portable electric flow pumps can reduce operating energy consumption and provide support for emergency operations.
Wu [2] found that as the blade installation angle decreases, the cavitation performance of the axial flow pump will become better, and the cavitation area on the blade surface will gradually decrease.Wang [3] used variable pitch technology to reduce the blade angle of the axial flow pump, thereby improving its cavitation performance and obtaining better operating stability.Ye [4] studied and found that the critical cavitation margin of swept impeller pumps is reduced.Zhao [5] found that the existence of discontinuous protrusions on the back of the blade can effectively block the impact of the return jet, control the shedding of cavitation, and at the same time inhibit the generation of tip vortex cavitation in the impeller flow channel.Zhi [6] found through experiments that the positive inlet guide vane angle will change the cavitation performance of the pump, and the negative guide vane angle hinders the cavitation performance.
Up to now, a large number of researchers have optimized the hydraulic performance of axial flow turbines or axial flow pumps.Peng [7,8] combined multi-objective optimization strategies and quasi-three-dimensional inverse problem design methods to optimize axial flow turbines, which significantly improved the hydraulic performance of the unit.Yan [9] used genetic algorithm combined with response surface function to optimize the design of axial flow pump guide vanes in view of hydraulic efficiency and other objectives.LI [10] optimized the cavitation performance of an axial flow pump using the response surface method.Liu [11] optimized the design of the axial flow pump and considered the control of flow separation to improve the cavitation performance of the unit.Zhu [12] and Wu [13] optimized the axial blood flow pump and improved the stability of the pump.
For the performance of the axial flow pump, the traditional optimization method is time-consuming and labor-intensive.This article analyzes the flow field characteristics and cavitation performance of the portable axial flow pump, and proposes a multi-structural parameter optimization scheme that integrates head and efficiency targets.The ISIGHT optimization platform was used to realize the parametric axial flow pump modeling and simulation process, and an intelligent optimization algorithm was used to perform multi-objective optimization of the axial flow pump structural parameters, and a specific optimization plan was determined.

Numerical method
The axial flow pump is numerically studied by ANSYS CFX, and the control equation is [14]: The expression of the Zwart cavitation model is where R b is 1x10 -6 m; C e is 50, and C c is 0.01.
The total entropy production Spro in the entire calculation domain is the sum of direct dissipation entropy production The direct dissipation entropy production is directly obtained through numerical calculation.The generation of turbulent dissipative entropy can be obtained [15].
The formula for calculating wall entropy production is [14] where w τ is the wall shear stress, and p v is the velocity near the wall.

Computational model
The structural diagram of the portable electric axial flow pump is shown in Figure 1, which mainly includes the guide vane body, impeller, water inlet section and water outlet section.Some geometric parameters are shown in Table 1.
Table 1.Parameters of electric axial flow pump.

Grid processing
The ICEM-CFD software is used to divide the water inlet section, impeller and guide vane watersheds into hexahedral structure meshes.The meshing results are shown in Figure 2.After verification of grid independence, 7.14 million units were used for further optimization and simulation.

Boundary condition setting
The preprocessing settings are as follows: the impeller is in the rotating domain, the inlet section, guide vane and outlet section are in the static domain, and the reference pressure is zero; the turbulence model uses the SST k-ω model, the cavitation model uses the Zwart model; and the no-slip boundary condition is used between the walls, and the outer wall of the impeller is set is an anti-rotating wall.The calculation of external characteristics adopts the inlet total pressure boundary condition, the pressure is 1 atm and the mass flow outlet boundary condition is used.Add vapor when performing cavitation calculation, set the volume fraction of liquid medium to 1, the volume fraction of gaseous medium to 0, and the saturated vapor pressure to 3574 Pa.

Analysis of calculation results of the initial model
A comparison of the initial performance curves is shown in Figure 3.The high efficiency point of the original model will shift toward large flow rates.The cavitation data is calculated under the inlet condition of 1atm.It can be seen that the pump has already experienced cavitation under this scheme, and its performance has dropped significantly.

Optimal design
The axial flow pump is optimally designed by using the intelligent optimization method based on CFD and algorithm.The optimization process includes parametric 3D modeling, numerical simulation, approximate model building and algorithm optimization.The space is uniformly sampled using an optimal Latin hypercube.Combining ICEM and Turbo-Grid to divide the calculation domain into hexahedral grids, the number of grids is guaranteed to be consistent with the initial scheme.CFX is used to calculate the performance of the water pump, and then the numerical calculation results are approximated by radial basis neural network.Finally, the multi-island genetic algorithm is used to optimize the approximate model to find the optimal solution.Figure 4 shows the procedure of this optimization.

Figure 4
Procedure of the optimization design.This optimization takes the maximum average efficiency under the three flow conditions of 0.9 Q d , 1.0 Q d , and 1.1Q d as the optimization goal, which can be described as: where

Sensitivity analysis
The RBF model is built using 250 sampling points.Figure 6 shows the results of DOE, the maximum head difference exceeds 4m, and the efficiency fluctuation range is greater than 4%, indicating that the value range of variables is valid.

Optimization results
Through the multi-island genetic algorithm, 20 islands are set, 10 times of inheritance are performed, and the final number of optimizations is 4000 times.After optimization, the optimal model is obtained.Comparison of initial and optimized geometric parameters is shown in Table 4.
Table 4. Ranges of optimization parameters.8 is the performance curve without considering cavitation.The water head of the optimized scheme is not much different from that of the initial scheme, and the efficiency under design conditions is increased by 6.3%. Figure 9 shows the comparison of the velocity streamlines of the cylindrical expansion surface with different flow rates and blade height positions before and after optimization.It can be seen that shedding vortices are prone to occur in the guide vane flow channel before optimization, and the impeller blade surface has a large angle of attack and is prone to loss.After optimization, the vane angle matches the liquid flow angle better, and the flow separation vortex in the guide vane channel is also improved.Figure 10 is the flow loss analysis of the diffuser and impeller.The flow losses in the diffuser are greater than those in the impeller.Under design conditions, the EPT of the diffuser and impeller were reduced by 70.2% and 25.3% respectively.The reduction of entropy production in the impeller is the main reason for the increase in efficiency.

Experimental verification
Based on the optimization results, a test prototype was produced and tested on site (Figure 16) to verify the precision and accuracy of the numerical simulation.Figure 18 shows the comparison of experimental and simulation results.The maximum relative error between the test and numerical simulation head and efficiency is less than 5%.The deviations of head and efficiency under design conditions are 1.42% and 4.52%, respectively, and the difference is small, which shows that the optimization results are good and the performance of the axial flow pump has been significantly improved.

Conclusions
First, based on the Zwart cavitation model, the overall performance and cavitation performance of the electric axial flow pump are analyzed.Then based on the ISIGHT intelligent optimization platform, the performance of the electric axial flow pump is optimized.Finally, the reliability of the optimization was verified through experimental testing.This article draws the following conclusions: (1) The efficiency of the optimized electric axial flow pump is increased by 6.3%, and the simulated data corresponds to the experimental data.At the same time, the optimized cavitation performance is significantly improved compared with the initial scheme.
(2) Entropy production can effectively predict the flow loss distribution of the electric axial pump.The incident loss and split flow inside the optimized electric axial flow pump are significantly improved, and the overall turbulent vortex dissipation and entropy generation of the pump are significantly reduced.
(3) The optimization method in this paper can be applied to the optimization of other fluid machinery, and more optimization parameters can be studied.

Figure 1 .
Figure 1.Structural diagram of electric axial flow pump.

Figure 3 .
Figure 3. Head and efficiency curves of the initial scheme.

Figure 6 .
Results of DOE.

Figure 7
shows the optimization results affected by the optimization variables.The results show that D, Z, β 2h are significantly positively correlated with the design head.But the effects of φ dh , φ ds and α 3h on the head can be ignored.The blade exit crown angle β 2s has the most positive impact on the efficiency of the pump.(a) H.(b) Eff.

Figure 8 .
Figure 8. Performance curve before and after optimization.Figure9shows the comparison of the velocity streamlines of the cylindrical expansion surface with different flow rates and blade height positions before and after optimization.It can be seen that shedding vortices are prone to occur in the guide vane flow channel before optimization, and the impeller blade surface has a large angle of attack and is prone to loss.After optimization, the vane angle matches the liquid flow angle better, and the flow separation vortex in the guide vane channel is also improved.

Figure 10 .Figure 11 .
Figure 10.Analysis of total loss.Figure11shows the comparison of entropy production loss distribution at different sections.The loss distribution of the impeller and guide vane parts of the original scheme was relatively large.After optimization, the loss distribution at different cross-sections was significantly reduced, and the effect of optimization was very obvious.

Figure 12 andFigure 12 .
Figure 11.Comparison of 1.0Qd loss distribution (left: original scheme, right: optimized scheme).Ideally, the blades of an axial flow pump indicate that there should be no radial flow.Excessive radial flow will cause mutual disturbance of the flow between the cylindrical layers, reducing the normal working ability of the blade.Figure12and Figure13compare the flow on the working face and back of the blade.Before optimization, obvious radial flow appeared on the surface of the blade near the hub in the design condition.After optimization, the vortex scale on the blade surface decreases, especially at the design point, there is almost no radial flow on the blade surface, and the impeller efficiency increases.

Figure 14
Figure14is a comparison of pump performance curves considering cavitation.The cavitation suppression effect of the optimized pump is very obvious, and the efficiency of the optimization scheme is increased by more than 20% under design conditions.

Figure 14 .
Figure 14.Comparison of cavitation performance before and after optimization.Figures 15 and 16 show the comparison of the cavitation volume fraction of the impeller flow channel and blade surface before and after optimization.After optimization, the cavitation volume on the back of the impeller and blades is significantly reduced.Only the gaps at the top of the blade and the back of the inlet edge are small, and a small amount of cavitation appears in this area, which has almost no impact on the impeller performance.

Figure 15
Figure 15 10% void volume fraction in the impeller channel.

Figure 16 .
Figure 16.10% cavitation volume fraction on the blade surface.

Figure 17 .
Figure 17.Experimental measurement.Figure18shows the comparison of experimental and simulation results.The maximum relative error between the test and numerical simulation head and efficiency is less than 5%.The deviations of head and efficiency under design conditions are 1.42% and 4.52%, respectively, and the difference is small, which shows that the optimization results are good and the performance of the axial flow pump has been significantly improved.

Figure 18 .
Figure 18.Comparison of experimental and simulated performance.

Table 3 .
Ranges of parameters.